The power 2 (or exponent 2) is the inverse of the square root:
√x*√x = (√x)² = x
What is the inverse of the square root?
The square root of a number X, gives a number Y such that the product between Y and itself is equal to X, this means that:
if:
√x = y
Then:
y*y = x
So we could write:
√x*√x = (√x)² = x
So the exponent 2 is the inverse of the square root.
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(4, -13) and (8,-8) slope formula
Point A (4, -13)
Point B (8, -8)
Slope formula
[tex]\begin{gathered} m=\frac{-8-(-13)}{8-4} \\ m=\frac{-8+13}{4} \\ m=\frac{5}{4} \\ \end{gathered}[/tex]The slope would be 5/4
The complex number w is given by w= p-4i/2-3i where p is a real constant. Express w in the form a+bi where a and b are real constants. give your answer in simplest terms of p.b) given that arg w= pi/4 find the value of p
Step 1
Given;
[tex]w=\frac{p-4i}{2-3i}[/tex]Required; To express w in the form of a+bi.
Step 2
Express w in the form of a+bi
Multiply the numerator and the denominator by the binomial conjugate of (2-3i)
The binomial conjugate of (2-3i) = (2+3i)
[tex]w=(\frac{p-4i}{2-3i})\times(\frac{2+3i}{2+3i})=\frac{2p+3pi-8i-12i^2}{4+6i-6i-9i^2}[/tex][tex]\begin{gathered} w=\frac{2p+3pi-8i-12(-1)}{4-9(-1)} \\ \text{Note; i}^2=(\sqrt[]{-1})^2=-1 \end{gathered}[/tex][tex]\begin{gathered} w=\frac{2p+3pi-8i+12}{4+9}=\frac{2p+3pi-8i+12}{13} \\ w=\frac{(2p+12)+(3p-8)i}{13} \\ w=\frac{(2p+12)}{13}+\frac{(3p-8)i}{13} \\ w=\frac{2(p+6)}{13}+\frac{(3p-8)i}{13} \end{gathered}[/tex]where;
[tex]\begin{gathered} a=\frac{2(p+6)}{13}_{} \\ bi=\frac{(3p-8)i}{13} \end{gathered}[/tex]According to Greg, perfect cherry pies have a ratio of 240 cherries to 3 pies. How many cherries does Greg need to make 15 perfect cherry pies?
Answer: 1200 cherries.
Step-by-step explanation:
If 240 cherries are need for 3 pies, multiply 240 by 5 to get the answer.
Your answer is 1200 cherries.
Greg needs 1200 cherries to make 15 perfect cherry pies.
35Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What istprobability that he will guess the first number correctly and the second number incorrectly?OAOB.olaroc.OD.ResetSubmit
Answer:
A. 5/36
Explanation:
The total number of possible number choice = 6
Only 1 out of 6 can be correct, thus:
[tex]P(\text{he will guess the first number correctly)}=\frac{1}{6}[/tex]There are 5 incorrect numbers, therefore:
[tex]P(\text{he will guess the }\sec ond\text{ number incorrectly)}=\frac{5}{6}[/tex]Therefore, the probability that he will guess the first number correctly and the second number incorrectly:
[tex]\begin{gathered} =\frac{1}{6}\times\frac{5}{6} \\ =\frac{5}{36} \end{gathered}[/tex]The correct choice is A.
Kite ABDC is shown. What is the value of x?
In a kite, one diagnal bisects the angle its passes through. This means that
4x - 5 = 2x + 35
4x - 2x = 35 + 5
2x = 40
x = 40/2
x = 20
For the given kite ABDE, the value of x will be 20. Option D is correct.
What is quadrilateral?It is defined as a four-sided polygon in geometry having four edges and four corners.
It is given in the figure, the two angles are (4x-5) and (2x+35).
Since the kite has two sets of congruent sides, we know it is a quadrilateral. It has a single pair of incongruent, opposing angles. A kite's diagonals are perpendicular. One diagonal is split in half. Although the top and bottom angles are divided in half, the diagonals are not congruent.
One diagonal in a kite divides the angle it traverses. It follows that
4x - 5 = 2x + 35
4x - 2x = 35 + 5
2x = 40
x = 40/2
x = 20
Thus, for the given kite ABDE, the value of x will be 20. Option D is correct.
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Does the table show direct variation? If so, state the constant of variation.
Okay, here we have this:
Considering the provided table, we are going to analize if the table shows direct variation, so we obtain the following:
To identify if there is direct variation then we will calculate the ratios between the points, and if they are all the same then the table does show direct variation, then we have:
y=kx
k=y/x
5/2=2.5
45/18=2.5
80/30=2.66
Since the ratios between the points are not the same, then it does not represent a direct variation.
A point is plotted on a coordinate grid at (-3, 4). How far is the point from point (0, 0)?
The point at (-3, 4) is at a distance of 5 units from the point (0, 0).
How far is the point from (0, 0)?For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:
distance = √( (x₁ - x₂)² + (y₁ - y₂)²)
In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:
distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5
The distance is 5 units.
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The length of a rectangle i 5 centimeters more than the width. The area of the rectangle is 36 square centimeters. What is the length?
Answer: 9 cm
Step-by-step explanation:
l=length. A=area. w=width.
l*w=A
l*(l-5)=36 ==> w=l-5
l^2-5l=36
l^2-5l-36=0
l^2-9l+4l-36=0
l(l-9)+4(l-9)=0
(l+4)(l-9)=0
9*4=36
4=9-5 ==> w=l-5
l=9 cm
Jane wants to make a a cake for her friend's birthday she had $9 and spent it on decoration with tax included a pack of 10 candles is $1.50 and which tube of of colored frosting is 2.75 if she has to bye two packs and candles how many tubes of frosting can she buy ?
Given:
Total money she had = $9
Cost of each pack of candles = $1.50
Cost of each tube of colored frosting = $2.75
Let's find the number of colored frosting she can buy.
Since she has to buy 2 packs of candles, the total cost she would spend on candles is:
Cost of candles = $1.50 x 2 = $3.00
Thus, we have the inequality:
2.75x + 3.00 ≤ 9
Where x represents the number of tubes of colored frosting she can buy.
Let's solve for x.
2.75x + 3 ≤ 9
Subtract 3 from bith sides:
2.75x + 3 - 3 ≤ 9 - 3
2.75x ≤ 6
Divide both sides by 2.75:
[tex]\begin{gathered} \frac{2.75x}{2.75}\le\frac{6}{2.75} \\ \\ x\le2.18 \end{gathered}[/tex]Since x is less than or equal to 2.18, this means Jane can buy no more than 2 tubes of colored frosting.
ANSWER:
No more than 2 tubes
a square base pyramid is shown below. find its surgace area. Round to the nearest tenth
Given data
Height = 16.8 ft
Slant height = 19.3 ft
First, you find the base of the right angle triangle in the daigram.
Opposite = 16.8 ft
Hypotenuse = 19.3 ft
Adjacent = b
[tex]\begin{gathered} \text{Appy pythagorus theorem} \\ \text{Opp}^2+Adj^2=Hypotenuse^2 \\ 16.8^2+b^2=19.3^2 \\ 282.24+b^2\text{ = 372.49} \\ b^2=372.49\text{ - 282.24} \\ b^2\text{ = 90.25} \\ b\text{ = }\sqrt[\square]{90.25} \\ b\text{ = 9.5} \end{gathered}[/tex]Next,
The side of the base of the pyramid = 2 x b
= 2 x 9.5
= 19
The square measure 19 ft
To find the surface area of the pyramid, sum the areas of the square base and the area of the four triangles.
Area of the square = 19 x 19 = 361
[tex]\begin{gathered} \text{Area of the four triangles = }\frac{1}{2}\text{ base x height} \\ \text{ = 0.5 x 19 x 19.3} \\ \text{ = 183.35} \\ \text{Area of the four triangle = 4 x 183.35 = 733.4} \end{gathered}[/tex]Toal surface area of the figure = 733.4 + 361
= 1094.4
Which of the following statements is NOT true regarding an expression written in scientific
notation in the form of ax10*?
O The value of a must be greater than or equal to 1 and smaller than 10.
O The value of n must be an integer.
O Doubling n results in a doubling of the value of the expression.
O Doubling a results in a doubling of the value of the expression.
Step-by-step explanation:
not true is " doubling n results in a doubling of the value of the expression".
e.g.
2.3 × 10² = 230
now I double n :
2.3 × 10⁴ = 23,000
the value of the expression has increased much more than just doubling.
Question 15 of 15Taniah is trying to find the area of the following square whereWY=10. What is the area?
The area of a square given its diagonal (d) is computed as follows:
[tex]A=\frac{1}{2}d^2[/tex]In this case, the diagonal is 10 units long, then the area is:
[tex]\begin{gathered} A=\frac{1}{2}\cdot10^2 \\ A=\frac{1}{2}\cdot100 \\ A=50\text{ square units} \end{gathered}[/tex]Calculate the area of each figure. Which figure has the greatest area? 9 cm 6.8 cm 7 cm l-_- 10 cm 15 cm 6 cm 13 cm
For the frst one is: 63 cm^2
[tex]A_{F1}=\text{ 9cm}\cdot7\operatorname{cm}=63cm^2[/tex]For the second figure we have that the area is: 136cm^2
[tex]\begin{gathered} A_{F2}=2\cdot(6.8cm)(10cm) \\ =2(68cm^2)\text{ = 136}cm^2 \end{gathered}[/tex]And for the third one, the area is: 84cm^2
[tex]\frac{(15cm\text{ + 13cm)}\cdot6\operatorname{cm}}{2}=\frac{28\operatorname{cm}\cdot6\operatorname{cm}}{2}=\frac{168\operatorname{cm}^2}{2}=84\operatorname{cm}[/tex]Thor goes to the store and buys a game station for $75. The store is running a discount of 10% What is the price of the game station after the discount?
To find the price after the discount, find at first, the amount of discount then subtract it from the original price
Since the discount is 10% of $75, then
Change 10% to decimal by divide it by 100, then multiply it by 75
[tex]\begin{gathered} \frac{10}{100}\times75=0.1\times75 \\ =7.5 \end{gathered}[/tex]The discount is $7.5
Subtract it from $75 to find the price after the discount
The price after discount = 75 - 7.5 = 67.5
The price after the discount is $67.5
ABC-DEF. what is the scale factor of triangle ABC to triangle DEF
in the given triangles the scale factor will be the ratio of the hypotenuse of DEF and the hypotenuse of ABC
so ratio = 30/10 = 3
thus the scale factor is 3
so the value of the sides of ABC is,
x = 27/3
x = 9
y = 18/3
y = 6
4. Jacob bought some tickets to see his favorite group, and it cost $76. The relationship between the adult tickets, a, and the student's tickets, s, can be expressed by the equation 10a + 8C = 76. If he bought 4 adult ticket, then how student's tickets did he buy? If he bought 2 student ticket, then how adult's tickets did he buy? Which equation shows the number of student tickets as a function of the number of adult tickets? A. C= 68 – 10a B.C=76 – 10a C. C= -4/5a +38/5 D. C=-5/4a+19/2
Given the equation:
[tex]10a+8c=76[/tex]If Jacob bought 4 adult tickets, then a = 4, so we can solve for c:
[tex]\begin{gathered} a=4 \\ \Rightarrow10(4)+8c=76 \\ \Rightarrow8c=76-40=36 \\ \Rightarrow c=\frac{36}{8}=\frac{9}{2}=4.5 \\ c=4.5 \end{gathered}[/tex]therefore, Jacob bought 4 or 5 students tickets.
Now, if Jacob bought 2 student tickets, then c=2 and for 'a' we have the following:
[tex]\begin{gathered} c=2 \\ \Rightarrow10a+8(2)=76 \\ \Rightarrow10a=76-16=60 \\ \Rightarrow a=\frac{60}{10}=6 \\ a=6 \end{gathered}[/tex]therefore, Jacob bought 6 adult tickets.
Finally, to find the equation that shows the number of student tickets as a function of adult tickets, we have to solve for 'c' to get the following:
[tex]\begin{gathered} 10a+8c=76 \\ \Rightarrow8c=76-10a \\ \Rightarrow c=-\frac{10}{8}a+\frac{76}{8}=-\frac{5}{4}a+\frac{19}{2} \\ c=-\frac{5}{4}a+\frac{19}{2} \end{gathered}[/tex]therefore, the function would be c = -5/4a +19/2
write equation in standard form
y= - 9/11x- 4
The standard form of the linear equation y = -9/11x - 4 is 9x + 11y = -44.
What is the given equation in standard form?The standard form of a linear equation is expressed as;
Ax + By = C
Where A and B are the coefficient of x and y respectively, C is the constant term.
Given the equation in the question;
y = -9/11x - 4
First, get rid of the fraction by multiplying both sides by //
11( y ) = 11( -9/11x - 4 )
Apply distributive property
11y = -9x - 44
Now, move all terms containing variables to the left and side of the equation.
11y + 9x = -44
Reorder the equation in form of Ax + By = C
9x + 11y = -44
Therefore, the standard form of the equation is 9x + 11y = -44
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Naomi is driving on a long road trip. She currently has 10 gallons of gas in her car. Each hour that she drives, her car uses up 0.75 gallons of gas. How much gas would be in the tank after driving for 4 hours? How much gas would be left after t hours?
7 Gallons of gas would be in the tank after driving for 4 hours. And,
10 - 0.75t gas would be left after t hours.
We have given that the total amount of gas in her car is 10 gallons and the car consumes 0.75 gallon per hour.
First we will determine the amount of gas left in the car after driving for four hours.
Since 0.75 gallon is consumed in an hour, to find the amount of gas consumed in 4 hours we will multiply the amount consumed in an hour to 4 hours.
That would be 0.75 × 4 = 3 Gallons of Gas
Now, the amount of gas left is simply the difference between the initial amount of gallons in the car and the amount of gallons spend in 4 hours.
That would be 10 - 3 = 7 Gallons of Gas
Now with the help of above concept, we will determine the amount of gas left after t hours.
Since 0.75 is used up per hour, the amount used up in t hours would be 0.75 × t = 0.75t
Now, the amount of fuel that would be left in the car would be the difference between what we had initially and what was used up.
That would be 10 - 0.75t .
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In a battle, Iceman beings to freeze iron man's suit. By the end of the battle, Iron Man's suit dropped to -4.5 deF. If Iceman was able to decrease Iron Man's suit by 73.2. What temperature did Iron Man's suit start at?
By solving a linear equation, we can see that the initial temperature of the suit is 68.7F
What temperature did Iron Man's suit start at?
We know that at the end of the battle, Iron Man's suit was at a temperature of -4.5 degrees Fahrenheit.
We know that Iceman decreased Iron Man's temperature by 73.2 F, so, if the initial temperature of the suit is T, then we can write the linear equation:
T - 73.2F = -4.5F
We can solve this equation for T.
T = -4.5F + 73.2F = 68.7F
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The perimeter of an isosceles triangle is 30 cm. The length of each congruent side is 3cm more than the length of its base. Find the lengths of all the sides.
Given:
the perimeter of an isosceles triangle 30cm
The length of each congruent side is 3cm more than the length of its base.
Let the length of the base side = x
So, the length of each congruent side = x + 3
the perimeter is the sum of the lengths of the sides of the triangle
So,
[tex](x+3)+(x+3)+x=30[/tex]Solve the equation to find the value of x
[tex]\begin{gathered} x+3+x+3+x=30 \\ 3x+6=30 \\ 3x=30-6 \\ 3x=24 \\ \\ x=\frac{24}{3}=8 \end{gathered}[/tex]So, the length of the base side = 8 cm
And the length of each congruent side = 8 + 3 = 11 cm
So,
The lengths of all sides are: 11 cm, 11 cm and 8 cm
factoring is writing an expression as the product of two factors; what are those factors ? 6(5+3)
Given the expression 6(5+3)
The expression shows that 6 was factored out from the bracket
evaluate the expression in parenthesis
= 6(5+3)
= 6(8)
This shows that the factors of the expression are 6 and 8
Solve the system of equation by substitution. x=7y+45x-4y=-11
Mila, this is the solution:
x = 7y + 4
5x - 4y = -11
_________________
Step 1: Let's substitute x in the second equation and solve for y, as follows:
write the letter of the table that corresponds with the graph.Explain your answer.
for the table X :
for the table R :
For tabel V :
For tabel Q :
Write this as a decimal number.
1 hundred + 7 tens + 3 tenths + 8 thousandths
Answer:
Step-by-step explanation:
17.308
this is the decimaal
QUESTION 1
The ingredients for Apple Crumble cost you $1.45 per serving. If your bakery menu lists a price of $4.95 for your Apple Crumble, then what percent
of the sale goes to the food cost?
The percentage of sale that goes to the food cost is 341.3%.
The ingredients for Apple crumble cost = $1.45 per serving.
The selling price of the Apple crumble = $4.95
percentage of the sale that goes to the food cost = ?
according to the question, we formulate:
% sale that goes to the food cost = cost of ingredients/selling price of the apple crumble×100
% sale = 4.95/1.45 × 100
% sale = 3.41 × 100
% sale = 341.3%
Hence the percentage of sale that goes to the food cost is 341.3%.
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Krissy owns a burger restaurant in Chicago, Illinois. The number of burgers sold at Krissy's restaurant was 605 in June. The number sold in July was 20% more than the number sold in June. How many burgers did Krissy's restaurant sell in July? burgers.
Answer:
100% ~ 605
20% ~ 121
120% ~ 726
The restaurant sells 726 burgers in July.
I’m having trouble I need this answered, it is apart of my ACT prep guide
Question:
Solution:
According to the data of the problem, the series is given by the following expression:
[tex]\sum ^{\infty}_{n\mathop=1}\frac{n}{3^n}=\frac{1}{3^1}+\frac{2}{3^2}+\frac{3}{3^3}+\cdots[/tex]now, remember the ratio test:
Suppose we have the series
[tex]\sum ^{}_{}a_n[/tex]Define,
[tex]L\text{ =}\lim _{n\to\infty}|\frac{a_{n+1}}{a_n}|[/tex]Then,
if L<1, the series is absolutely convergent (and hence convergent).
if
L>1, the series is divergent.
if
L=1 the series may be divergent, conditionally convergent, or absolutely convergent.
Applying this definition to the given series, we obtain:
[tex]L\text{ =}\lim _{n\to\infty}|\frac{(n+1)3^n_{}}{n3^{n+1}_{}}|=\frac{1}{3}<1[/tex]then, the given series is absolutely convergent (and hence convergent). So that, we can conclude that the correct answer is:
Stephanie was making chocolate chip cookies the recipe called for 9 chocolate chip cookie if Stephanie had a total of 108 chocolate chips how many cookies could she make
Given :
the recipe called for 9 chocolate chip cookie
The total chocolate chips = 108
So, the number of cookies = 108/9 = 12
For which value(s) of x will the rational expression below be undefined? Check all that apply
Given:
[tex]\frac{(x+3)(x+6)}{x+7}[/tex]Required:
We need to find the value of x that makes the given expression is undefined.
Explanation:
Recall that a rational expression is undefined when the denominator is equal to zero.
The denominator of the given expression is x+7.
Equate it to zero.
[tex]x+7=0[/tex]Subtract 7 from both sides of the equation.
[tex]x+7-7=0-7[/tex][tex]x=-7[/tex]Final answer:
[tex]x=-7[/tex]Explain the difference between the two different function transformations represented by
f(x+2)
f(x-2)
Include an example of each using the parent cubic equation,
f(x) = x³
For full credit, include the following:
1.
A description of each transformation including direction and number of units
2.
3 cubic equations and one graph showing the 3 curves: f(x), f(x+ 2), and f(x - 2)
The difference between the functions is explained below
What are functions?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. The set of all pairs, also known as the function's graph, is the only way to express a function in a unique way. In science, engineering, and the majority of the branches of mathematics, functions are often utilized. Functions are allegedly "the principal objects of inquiry" in the majority of mathematical disciplines. Maps and mappings are other names for functions.
Two transformations of the function f(x) are given f(x+2) and f(x-2)
The first one increments the function by 2 and the next one decrements the function by 2.
Let us understand with the help of an example,
The function f(x) = x³
Then f(x+2) = (x+2)³ = x³ + 4x + 8
and f(x-2) = (x-2)³ = x³ - 4x + 8
We can clearly see that both functions expanded differently
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